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6.453 Quantum Optical Communication
Spring 2009
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October 30, 2008
6.453 Quantum Optical Communication
Lecture 15
Jeffrey H. Shapiro
Optical and Quantum Communications Group
www.rle.mit.edu/qoptics
6.453 Quantum Optical Communication - Lecture 15
! Announcements
! Pick up lecture notes, slides
! Teleportation
! Fidelity analysis of continuous-variable teleportation
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Quadrature Entanglement: Vacuum-Input Paramp
Type-II Phase-Matched
Degenerate Parametric
Amplifier
! Quadrature Variances:
! Quadrature-Difference Variances:
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Continuous-Variable Teleportation: the Xmtr
vacuum-input
paramp
loss
to rcvr
Alice
loss
message input
homodyne
homodyne
to rcvr
to rcvr
from Charlie
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Continuous-Variable Teleportation: the Rcvr
from xmtr
Bob
coherent state
EO
modulator
from xmtr
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Continuous-Variable Teleportation: Xmtr Details
! Inputs to the 50/50 Beam Splitter:
where
is in arbitrary state,
is in vacuum state
! Homodyne Detector Measurement Outcomes:
where
and
are in vacuum states
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Continuous-Variable Teleportation: Xmtr Details
! Homodyne-Measurement Signal-to-Noise Ratios
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Classical Information as Quantum Information
! Alice’s Classical Transmission:
! Quantum-Mechanical Equivalent:
where
and
are in vacuum states
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Continuous-Variable Teleportation: Rcvr Details
! Input to the EO Modulator: Strong coherent state
! Output from the EO Modulator: Coherent state
! Asymmetric Beam Splitter Input-Output Relation:
where
and
are in vacuum states
9
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Continuous-Variable Teleportation: Rcvr Details
! Parameter Choices:
! Quantum Input-Output Teleportation Relation:
where
is in the vacuum state
10
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Continuous-Variable Teleportation: Output State
! Wigner Characteristic Function of Output State:
where
is the squeezing level
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Output State Fidelity
! Fidelity Analysis:
! Coherent-State Input Special Case:
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Coming Attractions: Lecture 16 + Schedule Notes
! Lecture 16:
Quantum Cryptography
! Bennett-Brassard protocol
! Ekert protocol
! Schedule Notes:
! Term paper proposals are due Thursday, November 6
! Mid-term exam Thursday, November 6
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